Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations

TL;DR

This paper introduces a machine learning approach using Jacobi-Legendre polynomial expansions to efficiently predict charge densities in density functional theory, significantly reducing computational costs.

Contribution

The authors develop a novel grid-centered representation combining Jacobi and Legendre polynomials with linear regression for accurate charge density prediction in DFT.

Findings

Achieves DFT-level accuracy in charge density predictions

Reduces computational time for electronic structure calculations

Enables rapid energy landscape scanning

Abstract

Kohn-Sham density functional theory (KS-DFT) is a powerful method to obtain key materials' properties, but the iterative solution of the KS equations is a numerically intensive task, which limits its application to complex systems. To address this issue, machine learning (ML) models can be used as surrogates to find the ground-state charge density and reduce the computational overheads. We develop a grid-centred structural representation, based on Jacobi and Legendre polynomials combined with a linear regression, to accurately learn the converged DFT charge density. This integrates into a ML pipeline that can return any density-dependent observable, including energy and forces, at the quality of a converged DFT calculation, but at a fraction of the computational cost. Fast scanning of energy landscapes and producing starting densities for the DFT self-consistent cycle are among the applications of our scheme.